What is the answer to sqrt(1+x\sqrt{x^2+4)}=x+1 ?

The answer to sqrt(1+x\sqrt{x^2+4)}=x+1 is x=0

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sqrt(1+x\sqrt{x^2+4)}=x+1

1 + x x^{2} + 4 = x + 1

x = 0

Solution steps

1 + x x^{2} + 4 = x + 1

Square both sides:

1 + x x^{2} + 4 = x^{2} + 2 x + 1

1 + x x^{2} + 4 = x^{2} + 2 x + 1

Subtract

x^{2} + 2 x + 1

from both sides

1 + x x^{2} + 4 - (x^{2} + 2 x + 1) = x^{2} + 2 x + 1 - (x^{2} + 2 x + 1)

Simplify

- x^{2} + x^{2} + 4 x - 2 x = 0

Factor

- x^{2} + x^{2} + 4 x - 2 x : - x (x - x^{2} + 4 + 2)

- x (x - x^{2} + 4 + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - x^{2} + 4 + 2 = 0

Solve

x - x^{2} + 4 + 2 = 0 : x = 0

x = 0

Verify Solutions:

x = 0

True

The solution is

x = 0

9 y + 1 - y + 9 = 4

25 + 5 x + 3 x + 31 = 4

x + c^{2} + a = 2 b

\frac{x - 1}{4} = x - 4

\frac{4}{3 x ^{\frac{4}{3}}} = 0

What is the answer to sqrt(1+x\sqrt{x^2+4)}=x+1 ?
The answer to sqrt(1+x\sqrt{x^2+4)}=x+1 is x=0
Solve for x: sqrt(1+x\sqrt{x^2+4)}=x+1
The solution is x=0